cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A002257 Numbers k such that 13*4^k + 1 is prime.

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%I A002257 M3247 N1310 #40 Jun 07 2025 16:42:10
%S A002257 1,4,5,10,14,41,94,154,158,500,14140,19004,21928,44009,54629,57148,
%T A002257 260653,281228,342280,519448,749938,930866
%N A002257 Numbers k such that 13*4^k + 1 is prime.
%D A002257 H. Riesel, "Prime numbers and computer methods for factorization," Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.
%D A002257 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002257 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002257 Ray Ballinger, <a href="http://www.prothsearch.com/index.html">Proth Search Page</a>.
%H A002257 R. M. Robinson, <a href="https://doi.org/10.1090/S0002-9939-1958-0096614-7">A report on primes of the form k.2^n+1 and on factors of Fermat numbers</a>, Proc. Amer. Math. Soc., 9 (1958), 673-681.
%t A002257 Select[Range[2000],PrimeQ[13 4^#+1]&] (* _Harvey P. Dale_, Jan 22 2011 *)
%o A002257 (Magma) [ k: k in [1..800]|IsPrime(13*4^k+1)]; // _Vincenzo Librandi_, Nov 21 2010
%o A002257 (PARI) for(k=1,10^5,if(ispseudoprime(13*4^k+1),print1(k, ", "))); /* _Joerg Arndt_, Apr 07 2013 */
%Y A002257 See A032356 (n such that 13*2^n+1 is prime) for more terms.
%K A002257 nonn,more
%O A002257 1,2
%A A002257 _N. J. A. Sloane_
%E A002257 Added more terms (from A032356), _Joerg Arndt_, Apr 07 2013